The mathematical and statistical theories of radioimmunoassay have been under progressive development, refinement, and testing. In the past year, attention has focused on immunoradiometric assays, two-site immunoradiometric (labeled antibody) assays (sandwich assays), enzyme-mediated immunoassay techniques (EMIT), enzyme-linked immunosorbent assays (ELISA), and the labeled antibody membrane assay (LAMA). The chemical and mathematical equations describing these systems have been developed and used for computer simulation. Results provide a theoretical basis for the observed "paradoxical high dose hook effect" which occurs in many of these systems and suggests ways for improvement of these assay systems. The mathematical theory of optimization of RIA has been tested in practice and existing computer programs have been shown to be basically valid and useful guides to the experimentalist. Several new statistical methods for analysis of radioimmunoassay results have been developed.